The constraint language for lambda structures (CLLS) is an expressive language of tree descriptions which combines
dominance constraints with powerful parallelism and binding
constraints. CLLS was introduced as a uniform framework for defining
underspecified semantics representations of natural language
sentences, covering scope, ellipsis, and anaphora. This article
presents saturation-based algorithms for processing the complete
language of CLLS. It also gives an overview of previous results on
questions of processing and complexity.